A conventional bandgap voltage reference circuit is based on the addition of two voltage components having opposite and balanced temperature slopes.
FIG. 1 illustrates a symbolic representation of a conventional bandgap reference. It consists of a current source, 110, a resistor, 120, and a diode, 130. It will be understood that the diode represents the base-emitter junction of a bipolar transistor. The voltage drop across the diode has a negative temperature coefficient, TC, of about −2.2 mV/° C. and is usually denoted as a Complementary to Absolute Temperature (CTAT) voltage, since its output value decreases with increasing temperature. This voltage has a typical negative temperature coefficient according to equation 1 below:
                                          V            be                    ⁡                      (            T            )                          =                                            V                              G                ⁢                                                                  ⁢                0                                      ⁡                          (                              1                -                                  T                                      T                    0                                                              )                                +                                                    V                be                            ⁡                              (                                  T                  0                                )                                      *                          T                              T                0                                              -                                                    σ                *                                  KT                  q                                *                                  ln                  ⁡                                      (                                          T                                              T                        0                                                              )                                                                              ︸                Nonlinearity                                                    component              ⁢                                                          ⁢              A                                +                                                                      KT                  q                                *                                  ln                  ⁡                                      (                                                                  Ic                        ⁡                                                  (                          T                          )                                                                                            Ic                        ⁡                                                  (                                                      T                            0                                                    )                                                                                      )                                                                              ︸                Nonlinearity                                                    component              ⁢                                                          ⁢              B                                                          (                  Eq          .                                          ⁢          1                )            Here, VG0 is the extrapolated base emitter voltage at zero absolute temperature, of the order of 1.2V; T is actual temperature; T0 is a reference temperature, which may be room temperature (i.e. T=300K); Vbe(T0) is the base-emitter voltage at T0, which may be of the order of 0.7V; σ is a constant related to the saturation current temperature exponent, which is process dependent and may be in the range of 3 to 5 for a CMOS process; K is the Boltzmann's constant, q is the electron charge, Ic(T) and Ic(T0) are corresponding collector currents at actual temperatures T and T0, respectively.
The current source 110 in FIG. 1 is desirably a Proportional to Absolute Temperature (PTAT) source, such that the voltage drop across r1 is PTAT voltage. As absolute temperature increases, the voltage output increases as well. The PTAT current is generated by reflecting across a resistor a voltage difference (ΔVbe) of two forward-biased base-emitter junctions of bipolar transistors operating at different current densities. The difference in collector current density may be established from two similar transistors, i.e. Q1 and Q2 (not shown), where Q1 is of unity emitter area and Q2 is n times unity emitter area. The PTAT current or voltage is generated by reflecting across a resistor a voltage difference (ΔVbe) of the two forward-biased base-emitter junctions of transistors Q1 and Q2. The resulting ΔVbe, which has a positive temperature coefficient, is provided in equation 2 below:
                              Δ          ⁢                                          ⁢                      V            be                          =                                                            V                be                            ⁡                              (                                  Q                  1                                )                                      -                                          V                be                            ⁡                              (                                  Q                  2                                )                                              =                                    KT              q                        *                          ln              ⁡                              (                n                )                                                                        (                  Eq          .                                          ⁢          2                )            
FIG. 2 illustrates the operation of the circuit of FIG. 1. By combining the CTAT voltage, V_CTAT of diode 130 with the PTAT voltage, V_PTAT, from the voltage drop across resistor 120, it is possible to provide a relatively constant output voltage Vref over a wide temperature range (i.e. −50° C. to 125° C.). This base-emitter voltage difference, at room temperature, may be of the order of 50 mV to 100 mV for n from 8 to 50. To balance the voltage components of the negative temperature coefficient from equation 1 and the positive temperature coefficient of equation 2 a gain factor is required. This gain factor may be in the order of five to ten. The balancing of the two voltage components is known as “first order error correction.” Even if the two voltage components are well balanced, the corresponding reference voltage is not entirely flat over temperature as second order nonlinearity components A and B of equation 1 are not compensated. Nonlinearity components contribute to what is known as “curvature.”
Different methods are known to compensate for “curvature” errors. In U.S. Pat. No. 4,443,753 to McGlinchey, a correction current is given in the form of equation 3 below:
                    I_corr        =                              KT            q                    ⁢                      ln            ⁡                          (                              T                                  T                  0                                            )                                                          (                  Eq          .                                          ⁢          3                )            The correction current is generated from a voltage difference of two bipolar transistors, having the same emitter area, one biased with PTAT current and one with CTAT current. This correction current, proportional to a differential gain stage, is then subtracted from a Brokaw cell in order to compensate for the “curvature” error.
There are many similar methods and circuits adopted to compensate for second order temperature effects in bandgap voltage references. One issue with the prior approaches includes the compensation component, proportional to σ, in nonlinearity component A of equation 1, which is very strongly dependent on process parameters. One circuit with less process dependency is disclosed in US Patent Application Publication No. US 2008/0074172, to the same inventor as the present invention. In order to correct the second order errors, typically additional circuitry is introduced which adds to the process variability, size, and complexity of the bandgap reference design.